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# Boris is playing on the mall escalators. One escalator goes up, one goes down, and one is out of service; otherwise, they're all identical.

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Boris is playing on the mall escalators. One escalator goes up, one goes down, and one is out of service; otherwise, they're all identical. The up and down escalators go at the same speed. You can assume that Boris always runs at the same speed.

Boris can run up the up escalator in 6 seconds. He can run up the down escalator in 30 seconds. How many seconds does it take him to run up the out-of-service escalator?

Mar 11, 2021

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d / ( r  + e ) = 6         d / ( r- e ) = 30                 e = escalator speed      r = run speed

30 r - 30 e = d

6r + 6e = d      or          6e = d - 6r     <======  multiply by -5 and sub into top equation

d = 30r-5d + 30 r

6d   = 60 r

60 / 6 = d/r = 10 seconds      Varaax is correct ......I fell prey to my warning about time in distance calcs !

Mar 11, 2021
edited by ElectricPavlov  Mar 11, 2021
edited by ElectricPavlov  Mar 11, 2021
edited by ElectricPavlov  Mar 11, 2021

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This is kinda like the boat and current speed questions

(6 + 30)/ 2 = speed on still escalator = 18 seconds

Mar 11, 2021
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I don't think that is correct...

Shouldn't it be

2*(30/6)=10?

EDIT: oh no ep has been typing for quite a while i might get embarrassed.

EDIT 2: OH GOD NOW CPHILL IS HERE IMMA GET FLAMED

Varxaax  Mar 11, 2021
edited by Varxaax  Mar 11, 2021
edited by Varxaax  Mar 11, 2021
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Will check....thanx  V

ElectricPavlov  Mar 11, 2021
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d / ( r  + e ) = 6         d / ( r- e ) = 30                 e = escalator speed      r = run speed

30 r - 30 e = d

6r + 6e = d      or          6e = d - 6r     <======  multiply by -5 and sub into top equation

d = 30r-5d + 30 r

6d   = 60 r

60 / 6 = d/r = 10 seconds      Varaax is correct ......I fell prey to my warning about time in distance calcs !

ElectricPavlov Mar 11, 2021
edited by ElectricPavlov  Mar 11, 2021
edited by ElectricPavlov  Mar 11, 2021
edited by ElectricPavlov  Mar 11, 2021
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Redux for posterity....figured a simpler way while sleeping last night

RATES     Rate WITH escaltor   1 escalator / 6 sec     Rate against escalator  1 escalator / 30 seconds

NOW it is like the airplane/windspeed or  boat/ current speed calcualtions

rate on still escalator =     ( 1/6 + 1/30 ) / 2 = (6/30) /2 = 6/60 = 1 /10    = rate on still esc    ( 1 esc / 10 sec)

then time on still escalator = 10 sec

ElectricPavlov  Mar 12, 2021
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I had my  COVID vaccine this morning and have been breathing paint fumes the rest of the day.....that's what I'm gonna use for an excuse !!!!!   Haha

thanx Varxaax !

Mar 11, 2021
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Very nice solution, EP  !!!

I had my second COVID shot yesterday....it obviously DIDN'T  help my IQ  much....LOL!!!!

Maybe I  SHOULD breathe paint fumes  !!

CPhill  Mar 11, 2021
edited by CPhill  Mar 11, 2021
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Paint fumes gib me asthma attacks 0.0

CalTheGreat  Mar 12, 2021
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Gee you two got in quick!

I know none of my friends in Germany have theirs yet.  Not even the first one.

And very few in Australia have it.  Our supply of vaccine has been partially blocked by Italy.

Which is not all that unreasonable.   Europeans need it far more than we do.

Life is almost normal here in Australia.

Mar 11, 2021
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We  have a large supply.......what we DON'T  have is a high vaccination rate.......some  people  are still balking at getting the vaccine.......go figure   !!!!

CPhill  Mar 11, 2021
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Yea well, if half the population gets inoculated it might be enough to protect the other half as well.

It will certainly cut down on infection rates anyway, so the hospitals will have more chance of coping.

I will get inoculated when I am told to but I don't care how long away that is.

I hope our government starts demanding people are inoculated before they return, or visit Australia. I know that is being looked at.

Melody  Mar 11, 2021
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enjoy the conversation LOL!

Mar 11, 2021
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The vaccine has not been approved for kids yet, so unfortunately 12-year-old Cal will not be getting the vaccine anytime soon.

Mar 12, 2021